IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v64y2003i3p243-248.html
   My bibliography  Save this article

The finiteness of moments of a stochastic exponential

Author

Listed:
  • Grigelionis, Bronius
  • Mackevicius, Vigirdas

Abstract

It is well known that the stochastic exponential , of a continuous local martingale M has expectation EZt=1 and, thus, is a martingale if (Novikov's condition). We show that, for p>1, EZtp t} 0. As a consequence, we get that the moments of the stochastic exponential of a stochastic integral with respect to a Brownian motion are all finite, provided the integrand is a Brownian functional of linear growth.

Suggested Citation

  • Grigelionis, Bronius & Mackevicius, Vigirdas, 2003. "The finiteness of moments of a stochastic exponential," Statistics & Probability Letters, Elsevier, vol. 64(3), pages 243-248, September.
    • Handle: RePEc:eee:stapro:v:64:y:2003:i:3:p:243-248
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(03)00155-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Albert N. Shiryaev & Jan Kallsen, 2002. "The cumulant process and Esscher's change of measure," Finance and Stochastics, Springer, vol. 6(4), pages 397-428.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. David Criens & Lars Niemann, 2023. "Robust utility maximization with nonlinear continuous semimartingales," Mathematics and Financial Economics, Springer, volume 17, number 5, February.
    2. Lars Hansen & José Scheinkman, 2012. "Pricing growth-rate risk," Finance and Stochastics, Springer, vol. 16(1), pages 1-15, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Buchmann, Boris & Kaehler, Benjamin & Maller, Ross & Szimayer, Alexander, 2017. "Multivariate subordination using generalised Gamma convolutions with applications to Variance Gamma processes and option pricing," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2208-2242.
    2. Liuren Wu, 2006. "Dampened Power Law: Reconciling the Tail Behavior of Financial Security Returns," The Journal of Business, University of Chicago Press, vol. 79(3), pages 1445-1474, May.
    3. Uwe Kuchler & Stefan Tappe, 2019. "Option pricing in bilateral Gamma stock models," Papers 1907.09862, arXiv.org.
    4. Kais Hamza & Fima C. Klebaner & Zinoviy Landsman & Ying-Oon Tan, 2014. "Option Pricing for Symmetric L\'evy Returns with Applications," Papers 1402.1554, arXiv.org.
    5. Matthias R. Fengler & Helmut Herwartz & Christian Werner, 2012. "A Dynamic Copula Approach to Recovering the Index Implied Volatility Skew," Journal of Financial Econometrics, Oxford University Press, vol. 10(3), pages 457-493, June.
    6. Anastasia Ellanskaya & Lioudmila Vostrikova, 2013. "Utility maximisation and utility indifference price for exponential semi-martingale models with random factor," Papers 1303.1134, arXiv.org.
    7. Nacira Agram & Bernt Øksendal & Jan Rems, 2024. "Deep learning for quadratic hedging in incomplete jump market," Digital Finance, Springer, vol. 6(3), pages 463-499, September.
    8. Fontana, Claudio & Gnoatto, Alessandro & Szulda, Guillaume, 2023. "CBI-time-changed Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 323-349.
    9. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2016. "A general HJM framework for multiple yield curve modelling," Finance and Stochastics, Springer, vol. 20(2), pages 267-320, April.
    10. David Criens & Kathrin Glau & Zorana Grbac, 2017. "Martingale property of exponential semimartingales: a note on explicit conditions and applications to asset price and Libor models," Post-Print hal-03898993, HAL.
    11. Mahdieh Aminian Shahrokhabadi & Alexander Melnikov & Andrey Pak, 2024. "The Duality Principle for Multidimensional Optional Semimartingales," JRFM, MDPI, vol. 17(2), pages 1-22, January.
    12. Alessandro Gnoatto, 2017. "Coherent Foreign Exchange Market Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-29, February.
    13. Küchler Uwe & Tappe Stefan, 2009. "Option pricing in bilateral Gamma stock models," Statistics & Risk Modeling, De Gruyter, vol. 27(4), pages 281-307, December.
    14. S. Cawston & L. Vostrikova, 2010. "$F$-divergence minimal equivalent martingale measures and optimal portfolios for exponential Levy models with a change-point," Papers 1004.3525, arXiv.org, revised Jun 2011.
    15. Roman V. Ivanov, 2023. "On the Stochastic Volatility in the Generalized Black-Scholes-Merton Model," Risks, MDPI, vol. 11(6), pages 1-23, June.
    16. Ruf, Johannes, 2013. "A new proof for the conditions of Novikov and Kazamaki," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 404-421.
    17. David Criens, 2018. "Deterministic Criteria For The Absence And Existence Of Arbitrage In Multi-Dimensional Diffusion Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-41, February.
    18. Alev{s} v{C}ern'y & Johannes Ruf, 2020. "Simplified stochastic calculus via semimartingale representations," Papers 2006.11914, arXiv.org, revised Jan 2022.
    19. Claudio Fontana & Alessandro Gnoatto & Guillaume Szulda, 2021. "CBI-time-changed L\'evy processes for multi-currency modeling," Papers 2112.02440, arXiv.org, revised Jul 2022.
    20. Hardy Hulley & Johannes Ruf, 2019. "Weak Tail Conditions for Local Martingales," Published Paper Series 2019-2, Finance Discipline Group, UTS Business School, University of Technology, Sydney.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:64:y:2003:i:3:p:243-248. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.